Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

<image>

The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

<image>

Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON3):

Solution:
#!/usr/bin/env pypy3

def all_zero(A):
    for row in A:
        for e in row:
            if e != 0: return False
    return True

n, m = input().split(' ')
n = int(n)
m = int(m)

A = []

for _ in range(n):
    row = input().split(' ')
    row = list(map(int, row))
    A += [row]

moves = []

# produce a zero

min_elem = min(min(row) for row in A)

if min_elem > 0:
    if m >= n:
        for x in range(n):
            moves += [f"row {x+1}"]*min_elem
    else:
        for y in range(m):
            moves += [f"col {y+1}"]*min_elem

    for x in range(n):
        for y in range(m):
            A[x][y] -= min_elem

pivot = None

for x in range(n):
    for y in range(m):
        if A[x][y] == 0:
            pivot = (x, y)
            break

assert(pivot is not None)

pivot_x, pivot_y = pivot

for x in range(n):
    if x == pivot_x: continue
    f = A[x][pivot_y]
    moves += [f"row {x+1}"]*f
    for y in range(m):
        A[x][y] -= f

for y in range(m):
    if y == pivot_y: continue
    f = A[pivot_x][y]
    moves += [f"col {y+1}"]*f
    for x in range(n):
        A[x][y] -= f

if not all_zero(A):
    print(-1)
else:
    print(len(moves))
    print('\n'.join(moves))